Poor families will be unable to afford essential items such as food and fuel if the chancellor presses ahead with plans to break the historic link between inflation and welfare payments, a leading charity has warned.

Ahead of key negotiations that have divided the "quad" of senior ministers, pitching David Cameron and George Osborne against Nick Clegg and the Treasury chief secretary, Danny Alexander.

The Children's Society warns that families with disabled children could be among the hardest hit – a single parent with a severely disabled child could lose £1,124 as a result of a benefit freeze compared with an inflation-linked uprating of 5.7%.

On average, a low-income family with children spends 20% more on fuel than a household on a higher income. In the past year alone, fuel costs have risen by 18.9%. This means that such families are likely to lose their ability to purchase essentials if the coalition decides to separate inflation and benefits after a meeting of quad ministers on Thursday.

For the past 20 years, annual benefit increases in April have been based on the previous September's inflation rate. To offset price rises, low-income families should, the Children's Society calculates, get a boost of 5.7% in their benefits. However, this September's inflation rate was 5.2%.

Ministers say this is still far above what was expected and instead Tory sources have been pushing to either freeze benefits or only raise them by a fraction of September figure.

A low-income couple who get benefits to supplement their wages, the charity calculates, would lose £110 a year if ministers back a compromise to use a lower inflation rate of 4.5%, based on average inflation during the six months to September. If the benefits were only uprated with earnings growth of 2.5% they would lose more than £300.

The Children's Society chief executive, Bob Reitemeier, said: "If the government reduces the rate of benefit uprating, families already finding it hard to cope with spiralling costs will struggle to keep pace with rising inflation, pushing them over the edge.

"Tens of thousands more children risk being plunged into greater hardship. It is crucial that children in all low-income families are protected from rising inflation costs. The government must avoid making further savings off the backs of poor families that will scar the lives of far too many children."

Lib Dem sources made it clear that their ministers would be pressing hard in the quad to protect the poor. "We aren't the majority in the coalition," one warned.